A note on Fourier coefficients of Hecke eigenforms in short intervals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913344725712896 |
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| author | Gun, Sanoli Naik, Sunil |
| author_facet | Gun, Sanoli Naik, Sunil |
| contents | In this article, we investigate large prime factors of Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms in short intervals. One of the new ingredients involves deriving an explicit version of Chebotarev density theorem in an interval of length $\frac{x}{(\log x)^A}$ for any $A>0$, modifying an earlier work of Balog and Ono. Furthermore, we need to strengthen a work of Rouse-Thorner to derive a lower bound for the largest prime factor of Fourier coefficients in an interval of length $x^{1/2 + ε}$ for any $ε>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on Fourier coefficients of Hecke eigenforms in short intervals Gun, Sanoli Naik, Sunil Number Theory 11F11, 11F30, 11F80, 11N56, 11R45 In this article, we investigate large prime factors of Fourier coefficients of non-CM normalized cuspidal Hecke eigenforms in short intervals. One of the new ingredients involves deriving an explicit version of Chebotarev density theorem in an interval of length $\frac{x}{(\log x)^A}$ for any $A>0$, modifying an earlier work of Balog and Ono. Furthermore, we need to strengthen a work of Rouse-Thorner to derive a lower bound for the largest prime factor of Fourier coefficients in an interval of length $x^{1/2 + ε}$ for any $ε>0$. |
| title | A note on Fourier coefficients of Hecke eigenforms in short intervals |
| topic | Number Theory 11F11, 11F30, 11F80, 11N56, 11R45 |
| url | https://arxiv.org/abs/2405.04698 |